Solve x^14/x^6/frac{x^12{x^14}}

$$\frac { \frac { x ^ { 14 } } { x ^ { 6 } } } { \frac { x ^ { 12 } } { x ^ { 14 } } }$$

Evaluate

$$x^{10}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 14 to get 8.

$$\frac{x^{8}}{\frac{x^{12}}{x^{14}}}$$

Rewrite x^{14} as x^{12}x^{2}. Cancel out x^{12} in both numerator and denominator.

$$\frac{x^{8}}{\frac{1}{x^{2}}}$$

Divide x^{8} by \frac{1}{x^{2}} by multiplying x^{8} by the reciprocal of \frac{1}{x^{2}}.

$$x^{8}x^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$x^{10}$$

Differentiate w.r.t. x

$$10x^{9}$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 6 from 14 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{8}}{\frac{x^{12}}{x^{14}}})$$

Rewrite x^{14} as x^{12}x^{2}. Cancel out x^{12} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{8}}{\frac{1}{x^{2}}})$$

Divide x^{8} by \frac{1}{x^{2}} by multiplying x^{8} by the reciprocal of \frac{1}{x^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}x^{2})$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{10})$$

The derivative of ax^{n} is nax^{n-1}.

$$10x^{10-1}$$

Subtract 1 from 10.

$$10x^{9}$$